An endpoint theorem in generalized L-spaces with applications

Abstract

In this paper, we will introduce first the notions of measure of non-singletonsness (denoted by δ), δ-Cauchy sequence and δ-completeness inthe setting of generalized £-spaces. Main result of the paper is a new endpoint theorem in generalized £-spaces from which we will derive an order-theoretic Cantor theorem in such spaces. Some examples are also given to support our main result. Our results generalize some recent results in the literature. © 2015.